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Theorem 1 : A non-zero number has infinitely many multiples.Theorem 2 : A non-zero number has at least one divisor.Theorem 3 : There are infinitely many numbers.

Therefore, according to Theorems 1 & 3, the set of all multiples of (an infinity) must contain infinitely many numbers composed of 's and 's. Because of Theorem 2, these numbers have at least one divisor, and since they are infinitely many, there is a probability of that is a divisor of one of these numbers.

Theorem 1 : A non-zero number has infinitely many multiples.Theorem 2 : A non-zero number has at least one divisor.Theorem 3 : There are infinitely many numbers.

Therefore, according to Theorems 1 & 3, the set of all multiples of (an infinity) must contain infinitely many numbers composed of 's and 's. Because of Theorem 2, these numbers have at least one divisor, and since they are infinitely many, there is a probability of that is a divisor of one of these numbers.

I don't know if this is "mathematically" correct, though.

Both of these statements are wrong. The fact that a number has infinite integer multiples does not necessarily mean one of those integers will consist of the digits 0,1. Using the same logic we could reach the false conclusion that every positive integer has a multiple which consists solely of the digits 7,1 - which is not true.

Also, the multiples of n are divided by it because, well, they are multiples of it (this is how you defined them)... However, the fact that they are infinite does not necessarily mean n will divide one of them. Take, for example, the following infinite sequence of multiples:

Then this is an infinite sequence of multiples of seven, but none of them are divided by 5!